Howell, P. D. and Siegel, M. (2003) The evolution of a slender non-axisymmetric drop in an extensional flow. Journal of Fluid Mechanics . (Submitted)
An asymptotic method for analysing slender non-axisymmetric drops, bubbles and jets in a general straining flow is developed. The method relies on the slenderness of the geometry to reduce the three-dimensional equations to a sequence of weakly coupled, quasi-two-dimensional Stokes flow problems for the cross-sectional evolution. Exact solution techniques for the flow outside a bubble in two-dimensional Stokes flow are generalised to solve for the transverse flow field, allowing large non-axisymmetric deformations to be described. A generalisation to the case where the interior contains a slightly viscous fluid is also presented.
Our method is used to compute steady non-axisymmetric solution branches for inviscid bubbles and slightly viscous drops. We also present unsteady numerical solutions showing how the eccentricity of the cross-section adjusts to a non-axisymmetric external flow. Finally, we use our theory to investigate how the pinch-off of a jet of relatively inviscid fluid is affected by a two-dimensional straining cross-flow.
|Subjects:||D - G > Fluid mechanics|
|Research Groups:||Oxford Centre for Industrial and Applied Mathematics|
|Deposited By:||Peter Howell|
|Deposited On:||09 Aug 2004|
|Last Modified:||20 Jul 2009 14:18|
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